Though widely used, the celebrated Kaplan-Meier estimator suffers from a disadvantage: it may happen, and in small and moderate samples it often does, that even if the difference between two consecutive times t 1 and t 2 (t 1 < t 2 ) is considerably large, for the values of the Kaplan-Meier estimators KM (t 1 ) and KM (t 2 ) at these times we may have KM (t 1 ) = KM (t 2 ). Although that is a general problem in estimating a smooth and monotone distribution function from small or moderate

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... , in the context of estimating survival probabilities the disadvantage is particularly annoying. In the paper we discuss a local smoothing of the Kaplan-Meier estimator based on an approximation by the Weibull distribution function. It appears that Mean Square Error and Mean Absolute Deviation of the smoothed estimator is significantly smaller. Also Pitman Closeness Criterion advocates for the new version of the estimator.